Line segment covering of cells in arrangements

Matias Korman, Sheung Hung Poon, Marcel Roeloffzen

Research output: Chapter in Book/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)


Given a collection L of line segments, we consider its arrangement and study the problem of covering all cells with line segments of L. That is, we want to find a minimum-size set L′ of line segments such that every cell in the arrangement has a line from L′ defining its boundary. We show that the problem is NP-hard, even when all segments are axis-aligned. In fact, the problem is still NP-hard when we only need to cover rectangular cells of the arrangement. For the latter problem we also show that it is fixed parameter tractable with respect to the size of the optimal solution. Finally we provide a linear time algorithm for the case where cells of the arrangement are created by recursively subdividing a rectangle using horizontal and vertical cutting segments.

Original languageEnglish
Title of host publicationCombinatorial Optimization and Applications - 9th International Conference, COCOA 2015, Proceedings
EditorsDonghyun Kim, Weili Wu, Ding-Zhu Du, Zaixin Lu, Wei Li
PublisherSpringer Verlag
Number of pages11
ISBN (Print)9783319266251
Publication statusPublished - 2015
Externally publishedYes
Event9th International Conference on Combinatorial Optimization and Applications, COCOA 2015 - Houston, United States
Duration: 18 Dec 201520 Dec 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference9th International Conference on Combinatorial Optimization and Applications, COCOA 2015
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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